Leicester booked their play-off semi-final spot with a 32-20 win at home to London Irish and they will meet Harlequins at Welford Road on Saturday. Harlequins have a fine record there, having won on their last two visits, including by a 22-9 score in September.
"We had quite a few guys missing that day (the defeat to Harlequins) but this is a one-off game," Cockerill, Leicester's director of rugby, said.
"They are a good side but we are a pretty good side too. We are not going to be complacent. If it had been Northampton we might have been after our recent success against them.
"But we have struggled to beat Harlequins, they are a good team and dangerous across the board. We have got to be dead, dead right next week otherwise it's over for us. It will be a tasty and interesting contest."
Cockerill expects all his main players to be fit, including centre Anthony Allen (neck) and England and British and Irish Lions flanker Tom Croft (shoulder), who both went off injured during the win over London Irish.
Leicester scored five tries through Croft, Ben Youngs, Mathew Tait, Vereniki Goneva and Toby Flood, while Irish replied with three from Alex Corbisiero, Topsy Ojo and Marland Yarde.
Cockerill criticised the visitors, saying: "They came to cheat and chuck the ball around."
Irish director of rugby Brian Smith said he was proud of his players who had rattled the Tigers.
"Leicester showed what a class act they are, six Lions in a team chock full of internationals. We did not want to go through the motions and we made them work hard. They deserved their win and a home semi-final, but we asked the boys to rattle some cages and they did that. I am proud of the troops."